Answer

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**Hint:**We will subtract the smaller number from the larger number and then we will divide it by the smaller number to find out the required percentage change. Finally we get the required answer.

**Formula used:**Suppose we want to calculate the percentage change for a number ‘\[a\]’ where it is changed to ‘\[b\]’ such that ‘\[b > a\]’.

So, after the change, the number increased by \[(b - a)\].

Now, the rate of change in increase is \[ = \dfrac{{(b - a)}}{a}\].

So, the required percentage change in the increment is \[ = \dfrac{{(b - a)}}{a} \times 100.\]

**Complete Step by Step Solution:**

We have to calculate the percentage change of \[63\;to\;105.\]

So, the number \[63\] increased to \[105\].

Therefore, the increment from \[63\] to \[105\] is \[(105 - 63)\].

So, the increment is \[42\].

So, the increment \[42\] is changed over the initial number \[63\].

So, the rate of change after increment of the number \[63\] to \[105\]is\[ = \dfrac{{42}}{{63}}.\]

So, the percentage increase of the number from \[63\;to\;105\] will be as \[\left( {\dfrac{{42}}{{63}} \times 100} \right)\].

So, after complete the division, we get:

\[ \Rightarrow \dfrac{{42}}{{63}} = 0.6667(approx)\].

So, the percentage change in the numbers is\[ = \left( {0.6667 \times 100} \right)\].

So, the required percentage is \[66.67\% \].

**Therefore, the percentage change of \[63\] to \[105\] is \[66.67\% \].**

**Note:**Points to remember:

The changed number can be smaller than the given number.

In such cases, we need to check how much the given number is decreased under the changed number.

Suppose a number ‘\[a\]’ is changed to ‘\[b\]’ such that \[a < b\] and we are required to calculate the percentage change.

So, firstly we will calculate the decrement of the number.

Therefore, the number decrement is\[(b - a) = - (a - b)\], negative sign carries as it signifies the decrement.

Therefore, the percentage change will become\[ = \left( {\dfrac{{ - (a - b)}}{a} \times 100} \right)\].

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